一种改进的动态核主元分析故障检测方法

针对复杂工业系统动态非线性故障检测过程精度低和计算量大的问题,提出了一种改进的动态核主元分析故障检测方法,该方法首先利用不可区分度剔除相关程度较小或者不相关变量,减少数据量,然后通过观测值扩展对筛选后的新数据构建增广矩阵,并对矩阵使用核主元分析提取变量数据的非线性空间相关特征,最后通过监测T2和SPE两种统计量诊断出系统发生故障及识别故障变量。仿真实验证明,该方法能对风力发电机故障进行有效监测和诊断,与KPCA方法相比,改进的动态核主元分析方法对微小故障更为敏感。     

一种改进的动态核主元分析故障检测方法

针对复杂工业系统动态非线性故障检测过程精度低和计算量大的问题,提出了一种改进的动态核主元分析故障检测方法，该方法首先利用不可区分度剔除相关程度较小或者不相关变量,减少数据量，然后通过观测值扩展对筛选后的新数据构建增广矩阵，并对矩阵使用核主元分析提取变量数据的非线性空间相关特征，最后通过监测T ²和SPE 两种统计量诊断出系统发生故障及识别故障变量。仿真实验证明，该方法能对风力发电机故障进行有效监测和诊断，与KPCA方法相比，改进的动态核主元分析方法对微小故障更为敏感。     

基于双层局部KPCA的非线性过程微小故障检测方法

针对传统核主元分析（KPCA）方法难以有效检测微小故障的问题,提出一种基于双层局部核主元分析（double-level local kernel principal component analysis,DLKPCA）的非线性过程微小故障检测方法。该方法从变量和样本两个角度来挖掘数据内部的局部信息,以提高故障检测能力。首先,利用变量分块思想,基于不同变量与核主元之间互信息相关度的相似性,将所有过程变量划分多个局部变量块。然后,构建基于得分向量和特征值的残差函数以挖掘样本局部信息。最后利用贝叶斯融合策略对各块的结果进行融合。在田纳西-伊斯曼基准过程的仿真结果表明,在微小故障检测方面,本文所提方法具有比传统KPCA方法更好的故障检测性能。     

一种基于KNMF的非线性故障诊断方法

将核非负矩阵分解方法引入到过程监控中,设计了K2和SPE统计量反映原始数据的能量波动情况,进而检测过程故障的发生。同时提出一种KNMF贡献图计算方法,根据变量和非线性数据的相关性,计算变量贡献值并绘制贡献图,用于故障辨识。在TE模型上的仿真结果验证了KNMF故障检测的良好性能,利用KNMF贡献图可以较好地辨识故障变量。     

基于加权统计特征KICA的故障检测与诊断方法

针对核独立元分析（kernel independent component analysis, KICA）在非线性动态过程中对微小故障检测率低的问题,提出一种基于加权统计特征KICA（weighted statistical feature KICA, WSFKICA）的故障检测与诊断方法。首先,利用KICA从原始数据中捕获独立元数据和残差数据;然后,通过加权统计特征和滑动窗口获取改进统计特征数据集,并由此数据集构建统计量进行故障检测;最后,利用基于变量贡献图的方法进行过程故障诊断。与传统KICA统计量相比,所提方法的统计量对非线性动态过程中的微小故障具有更高的故障检测性能。应用该方法对一个数值例子和田纳西-伊斯曼（Tennessee-Eastman, TE）过程进行仿真测试,仿真结果显示出所提方法相对于独立元分析（ICA）、KICA、核主成分分析（kernel principal component analysis, KPCA）和统计局部核主成分分析（statistical local kernel principal component analysis, SLKPCA）检测的优势。     

基于WPRKPCA的非线性化工过程微小故障检测

传统核主元分析法（KPCA）是一种广泛应用的非线性化工过程故障检测方法,但是其未充分利用过程数据的概率分布信息,往往难以有效检测过程中的微小故障。针对传统KPCA方法的局限性,本文提出了一种基于加权概率相关核主元分析（WPRKPCA）的非线性化工过程微小故障检测方法。与传统KPCA方法监控核成分的变化不同,该方法利用Kullback Leibler散度（KLD）度量核成分的概率分布变化,进而建立基于KLD成分的统计监控模型,以充分挖掘过程数据所包含的概率信息。进一步考虑到不同KLD成分承载故障信息的差异性,该方法设计了一种基于核密度估计的指数加权策略,根据KLD成分描述故障信息程度的差异分配相应的权值,以加强监控模型对微小故障检测的灵敏性。在一个数值例子和连续搅拌反应器（CSTR）系统上的仿真结果表明,本文所提方法具有比传统KPCA方法更好的微小故障检测性能。     

基于小波去噪的FVS-KPCA故障检测方法

对于复杂非线性系统,实际得到的数据不可避免地带有噪声、随机干扰,而传统的核主元分析(KP-CA)方法应用于大样本集的故障检测,要计算核矩阵K很困难。为此,提出一种小波去噪与特征矢量选择-核主元分析(FVS-KPCA)相结合的故障检测方法,首先对数据进行小波去噪,再采用特征矢量选择(FVS)与KPCA结合的方法能有效降低故障检测计算的复杂性。把上述方法应用到Tennessee Eastman(TE)化工过程,仿真结果表明该方法能有效地提高故障检测的速度。     

基于加权统计局部核主元分析的非线性化工过程微小故障诊断方法

传统统计局部核主元分析（statistical local kernel principal component analysis, SLKPCA）在构造改进残差时未考虑样本的差异性,使得故障样本信息易于被其他样本所掩盖,针对该问题,提出一种基于加权统计局部核主元分析（weighted statistical local kernel principal component analysis, WSLKPCA）的非线性化工过程微小故障诊断方法。该方法首先利用KPCA获取过程的得分向量和特征值并构建初始残差。然后设计了一种基于测试样本与训练样本之间距离的加权策略构建加权改进残差,对含有较强微小故障信息的样本赋予较大权值,以增强故障样本的影响。最后,采用基于测量变量与监控统计量之间的加权互信息构建贡献图以识别故障源变量。在连续搅拌反应釜和田纳西伊斯曼（Tennessee Eastman, TE）化工过程上的仿真结果表明,所提方法具有良好的微小故障检测与识别性能。     

基于双层局部KPCA的非线性过程微小故障检测方法

针对传统核主元分析(KPCA)方法难以有效检测微小故障的问题,提出一种基于双层局部核主元分析(double-level local kernel principal component analysis,DLKPCA)的非线性过程微小故障检测方法。该方法从变量和样本两个角度来挖掘数据内部的局部信息,以提高故障检测能力。首先,利用变量分块思想,基于不同变量与核主元之间互信息相关度的相似性,将所有过程变量划分多个局部变量块。然后,构建基于得分向量和特征值的残差函数以挖掘样本局部信息。最后利用贝叶斯融合策略对各块的结果进行融合。在田纳西-伊斯曼基准过程的仿真结果表明,在微小故障检测方面,本文所提方法具有比传统KPCA方法更好的故障检测性能。     

基于小波核聚类的非高斯过程故障检测方法

针对工业过程检测变量具有的非线性和非高斯性等特点,提出了一种基于小波核聚类的核主元分析（WKPCA）方法来处理过程数据的非线性特性,同时引用支持向量数据描述（SVDD）对过程进行建模。本算法先根据Morlet小波具有多分辨分析和能以更高的精度逼近任意函数的特点,将其构建为小波核函数,可以增强KPCA的非线性核映射和抗噪能力,然后在映射后的特征空间中进行均值聚类分析,选择每个聚类中展现特征中心的数据,大大减少了核函数的计算量;最后通过SVDD提出监控指标来描述过程的非高斯特性。将上述方法用在一个标准仿真平台Tennessee-Eastman上,结果表明,该方法能及时有效地检测出系统产生的故障和异常情况。     

基于约翰逊转换的鲁棒化工过程监控方法

化工厂中一个小故障可能导致大事故,从而造成生命财产损失和环境破坏。为了防止小故障演变成大事故,化学工业需要有效的过程监控来及时检测故障和诊断故障原因。传统化工过程监控方法主元分析法(Principal Component Analysis, PCA)假设数据服从高斯分布,实践中有时并不满足该条件。此外,其使用方差、协方差捕捉数据非线性变化时,鲁棒性较差。本工作提出一种改进的主元分析法—基于约翰逊转换的鲁棒过程监控方法。首先引入约翰逊正态转换(Johnson Transformation)使过程数据服从高斯分布;其次使用鲁棒性强的斯皮尔曼相关系数(Spearman Correlation Coefficient)矩阵代替传统主元分析法的协方差矩阵提取特征向量,构造特征空间;最后将过程数据投影到特征空间,使用T2和SPE统计量实施过程监控。将此方法应用于TE过程故障案例,并与PCA和核主元分析法(Kernel Principal Component Analysis, KPCA)对比,验证了此方法的有效性。     

Fault identification for process monitoring using kernel principal component analysis

In this research, we develop a new fault identification method for kernel principal component analysis (kernel PCA). Although it has been proved that kernel PCA is superior to linear PCA for fault detection, the fault identification method theoretically derived from the kernel PCA has not been found anywhere. Using the gradient of kernel function, we define two new statistics which represent the contribution of each variable to the monitoring statistics, Hotelling's T²and squared prediction error (SPE) of kernel PCA, respectively. The proposed statistics which have similar concept to contributions in linear PCA are directly derived from the mathematical formulation of kernel PCA and thus they are straightforward to understand. The main contribution of this work is that we firstly suggest a fault identification method especially applicable to process monitoring using kernel PCA. To demonstrate the performance, the proposed method is applied to two simulated processes, one is a simple nonlinear process and the other is a non-isothermal CSTR process. The simulation results show that the proposed method effectively identifies the source of various types of faults.     

A sparse PCA for nonlinear fault diagnosis and robust feature discovery of industrial processes

Pearson's correlation measure is only able to model linear dependence between random variables. Hence, conventional principal component analysis (PCA) based on Pearson's correlation measure is not suitable for application to modern industrial processes where process variables are often nonlinearly related. To address this problem, a nonparametric PCA model is proposed based on nonlinear correlation measures, including Spearman's and Kendall tau's rank correlation. These two correlation measures are also less sensitive to outliers comparing to Pearson's correlation, making the proposed PCA a robust feature extraction technique. To reveal meaningful patterns from process data, a generalized iterative deflation method is applied to the robust correlation matrix of the process data to sequentially extract a set of leading sparse pseudoeigenvectors. For online fault diagnosis, the T² and SPE statistics are computed and analyzed with respect to the subspace spanned by the extracted pseudoeigenvectors. The proposed method is applied to two industrial case studies. Its process monitoring performance is demonstrated to be superior to that of the conventional PCA and is comparable to those of Kernel PCA and kernel independent component analysis at a lower computational cost. The proposed PCA is also more robust in sparse feature extraction from contaminated process data. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1494–1513, 2016     

Nonlinear process monitoring using kernel principal component analysis

In this paper, a new nonlinear process monitoring technique based on kernel principal component analysis (KPCA) is developed. KPCA has emerged in recent years as a promising method for tackling nonlinear systems. KPCA can efficiently compute principal components in high-dimensional feature spaces by means of integral operators and nonlinear kernel functions. The basic idea of KPCA is to first map the input space into a feature space via nonlinear mapping and then to compute the principal components in that feature space. In comparison to other nonlinear principal component analysis (PCA) techniques, KPCA requires only the solution of an eigenvalue problem and does not entail any nonlinear optimization. In addition, the number of principal components need not be specified prior to modeling. In this paper, a simple approach to calculating the squared prediction error (SPE) in the feature space is also suggested. Based on T² and SPE charts in the feature space, KPCA was applied to fault detection in two example systems: a simple multivariate process and the simulation benchmark of the biological wastewater treatment process. The proposed approach effectively captured the nonlinear relationship in the process variables and showed superior process monitoring performance compared to linear PCA.     

独立元子空间算法及其在故障检测上的应用

针对高维数据建模问题,提出一种独立元子空间算法(ICSM),作为一种新的集成学习算法,ICSM利用独立元在不同变量上的贡献度来选取子空间,符合了集成学习的要求,具备了明确的物理意义,有效地克服了随机子空间算法(RSM)的主要缺点。在此基础上,进一步将ICSM应用于工业过程监控,提出了一种新的ICSM-PCA故障检测算法。首先在各个子空间内分别建立相应的PCA监测模型,然后根据T~2和SPE统计量的值计算出集成时各自的权重,最后构造两个集成统计量对工业过程进行监测。通过在Tennessee Eastman(TE)模型上的仿真研究,说明提出的算法具有较好的建模效果和故障检测能力。     

A local and global statistics pattern analysis method and its application to process fault identification☆

Traditional principal component analysis (PCA) is a second-order method and lacks the ability to provide higher-order representations for data variables. Recently, a statistics pattern analysis (SPA) framework has been incor-porated into PCA model to make full use of various statistics of data variables effectively. However, these methods omit the local information, which is also important for process monitoring and fault diagnosis. In this paper, a local and global statistics pattern analysis (LGSPA) method, which integrates SPA framework and locality pre-serving projections within the PCA, is proposed to utilize various statistics and preserve both local and global in-formation in the observed data. For the purpose of fault detection, two monitoring indices are constructed based on the LGSPA model. In order to identify fault variables, an improved reconstruction based contribution (IRBC) plot based on LGSPA model is proposed to locate fault variables. The RBC of various statistics of original process variables to the monitoring indices is calculated with the proposed RBC method. Based on the calculated RBC of process variables' statistics, a new contribution of process variables is built to locate fault variables. The simula-tion results on a simple six-variable system and a continuous stirred tank reactor system demonstrate that the proposed fault diagnosis method can effectively detect fault and distinguish the fault variables from normal variables.     

Fault detection and diagnosis in a non-Gaussian process with modified kernel independent component regression

Quality-related fault detection and diagnosis are crucial in the data-driven process monitoring field. Most existing methods are based on principal component analysis (PCA) or partial least squares (PLS), which will miss high-order statistical information when the industrial process does not satisfy a Gaussian distribution. Meanwhile, the traditional contribution plot is difficult to directly apply to nonlinear processes in some cases due to its limitation of convergence. As such, a modified kernel independent component regression (MKICR) model, which considers high-order statistical information, is proposed for quality-related fault detection and faulty variable identification. First, the relationship between the independent components and quality variables is established by kernel independent component regression, and the correlation matrix is obtained. Then, the kernel independent components can be suitably divided into quality-related and quality-unrelated parts. Finally, an analysis of the contribution of each variable to the statistics based on Lagrange's mean value theorem is presented. In addition, a numerical case and the Tennessee Eastman process (TEP) demonstrate the efficacy and superiority of the proposed method.     

基于变量子域PCA的故障检测方法

针对工业过程监控中传统主元分析（PCA）方法没有突出局部变量信息的问题,提出一种基于变量子域PCA（variable sub-region PCA,VSR-PCA）的故障检测方法。首先使用PCA将原始数据空间分解成主元子空间（principal component subspace,PCS）和残差子空间（residual subspace,RS）,计算变量与PCS的互信息来度量两者的相关性并以此划分变量子域。然后在变量子域中计算局部T²统计量和局部SPE统计量,并通过贝叶斯推理整合所有子域的信息构造全局统计量,使得在利用所有过程信息的同时挖掘局部变量信息。在连续搅拌反应釜系统上的仿真结果表明,VSR-PCA方法具有更好的过程监控性能。     

基于最小充分统计量模式分析的故障检测方法

统计量模式分析（SPA）最近在故障检测领域取得了广泛应用,其实质是用数据的统计量矩阵来代替原始数据矩阵进行故障检测,然而其统计量的选取存在盲目性且各统计量之间存在复杂的非线性关联关系,难以满足后续应用主成分分析（PCA）完成故障检测所需的基本条件。为了解决这个问题,提出了基于最小充分统计量模式分析的故障检测方法（MSSPA）。该方法首先将原始数据矩阵进行正交变换以消除变量之间的关联性,然后估计出每个变量的概率密度函数或者多个变量的联合概率密度函数,进而求出原始数据的最小充分统计量,并用最小充分统计量来构造统计量矩阵。最小充分统计量的引入还能够有效应对数据的非高斯分布问题。最后,通过在TE过程上的仿真测试验证了该方法用于故障检测的可行性和有效性。